Optimal Timing to Trade along a Randomized Brownian Bridge

Abstract

This paper studies an optimal trading problem that incorporates the trader’s market view on the terminal asset price distribution and uninformative noise embedded in the asset price dynamics. We model the underlying asset price evolution by an exponential randomized Brownian bridge (rBb) and consider various prior distributions for the random endpoint. We solve for the optimal strategies to sell a stock, call, or put, and analyze the associated delayed liquidation premia. We solve for the optimal trading strategies numerically and compare them across different prior beliefs. Among our results, we find that disconnected continuation/exercise regions arise when the trader prescribe a two-point discrete distribution and double exponential distribution.

Discounted Optimal Stopping of a Brownian Bridge, with Application to American Options under Pinning

“…For example, in [21], the authors work in a non-discounted scenario with the identity as the gain function and gives bounds for the value function with a general pinning point distribution. Another good example is [25], where gain functions of class C 2 are considered.…”

“…The analytical results in [13] are extended in [24] by looking at a class of Gaussian bridges that share the same optimal stopping boundary. The discounted problem with a Brownian bridge and in the presence of random pinning point is addressed in [25], under regularity assumptions on the gain function that allow for an application of the standard Itô's formula (something that does not hold in our setting).…”

Editorial for Special Issue “Finance, Financial Risk Management and their Applications”

“…They demonstrated that financial disturbance may be created because of the potential for shadow banking activities to spill over to regular banking activities and damage the real economy. Finally, the tenth paper entitled "Optimal Timing to Trade along a Randomized Brownian Bridge" by Leung et al (2018) investigates an optimal trading problem that incorporates the trader's market view on the terminal asset price distribution and uninformative noise embedded in the asset price dynamics. The authors modeled the underlying asset price evolution by an exponential-randomized Brownian bridge and considered various prior distributions for the random endpoint.…”

Optimal stopping for the exponential of a Brownian bridge

“…Indeed, the exponential structure avoids the unpleasant feature of negative asset prices, whilst retaining the pinning effect discussed above. Questions concerning stopping the exponential of a Brownian bridge were also considered in [20] in a model inspired by financial applications. In fact, in [20] authors consider a more general model than ours and allow a random pinning point.…”

“…Questions concerning stopping the exponential of a Brownian bridge were also considered in [20] in a model inspired by financial applications. In fact, in [20] authors consider a more general model than ours and allow a random pinning point. However, the complexity of the model is such that the analysis is carried out mostly from a numerical point of view.…”